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Tyro
Asked: 2021-04-08T04:17:59+00:00 In: ,

Math: Parallelogram

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1. If m𝑊𝑋 ̅̅̅̅̅ = 6x cm, m𝑋𝑌̅̅̅̅ = 5y – 4 cm, m𝑌𝑍̅̅̅̅
= x + 35 cm and m𝑊𝑍 ̅̅̅̅̅ = y + 17 cm, then
what is the perimeter of parallelogram
WXYZ?
2. If m∠𝑋𝑊𝑌 = (3x + 11)O and m∠𝑍𝑌𝑊 =
(7x – 1)O, when m∠𝑍𝑊𝑌 = (2y + 2)O and
m∠𝑋𝑌𝑊 = (3x – 2)O, then what is m∠𝑊 and m∠𝑌?

 

 

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1 Answer

  2. acedstud
    1. A property of a parallelogram is that opposite sides are congruent (equal in length). Thus, using this property, we have that \overline{WX}\cong\overline{YZ}\Rightarrow6x=x+35\Rightarrow6x-x=35\Rightarrow5x=35\Rightarrow x=\dfrac{35}{5}=7.

    Similarly, \overline{XY}\cong\overline{WZ}\Rightarrow5y-4=y+17\Rightarrow5y-y=17+4\Rightarrow4y=21\Rightarrow y=\dfrac{21}{4}=5.25.

    Thus, the sides of the parallelogram are 6(7), 5(5.25) – 4, 7 + 35, 5.25 + 17 = 42, 22.25, 42, 22.25.

    The perimeter of a closed shape is the length of the outline, thus the perimeter of this parallelogram is 42 + 22.25 + 42 + 22.25 = 128.5 cm.

     

    2. Ask the second question separately to receive the answer.

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